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Buffer control in stochastic flow lines
| PhD student | Nora Krippendorff |
| Research area | Planning and control under uncertainty |
Summary
When using forming or machining production processes, the equipment is subject to mechanical stresses that can lead to wear-related malfunctions and decreasing system availability. Even brief malfunctions of this kind can lead to blockages and downtimes in series production and thus to production losses. However, these can be avoided or minimized by decoupling the production stages via workpiece buffers.
Dedicated buffers are usually used in a series production system, each of which decouples two successive production stages and holds their intermediate product. Buffer capacities can be used more efficiently if consolidated buffers are used jointly for several intermediate products. On the other hand, the conveying effort for the intermediate storage of the workpieces increases in this case.
As part of the buffer allocation, a given total capacity of buffer spaces must be allocated to a quantity of buffers to be determined and for each buffer it must be specified which intermediate products can use it. In principle, configurations are also conceivable in which several buffers are allocated to one intermediate product. The general problem of buffer allocation that we investigated consists of assigning a non-empty quantity of intermediates to each of the buffer locations. The objective of buffer allocation is often studied to maximize the production rate of the line at steady-state equilibrium. If the total capacity of the buffers is not predetermined but is the subject of planning, this is referred to as a buffer distribution problem, which is obtained from the buffer allocation problem if the allocation of an empty quantity of intermediate products is also permitted. In buffer allocation problems, imputed capital commitment costs for the resulting buffer stocks are typically also taken into account.
For configurations in which intermediate products have been allocated to several buffers, a buffer management problem also arises in addition to the tactical problem of buffer allocation or distribution at the operational level. Here, a decision must be made for these intermediate products as to when workpieces should be stored at which buffer location or removed from which buffer location in order to avoid blockages and idle times as far as possible. If discontinuous conveyors are used to transport the workpieces between the production line and buffer locations, a scheduling problem arises for the use of the conveyors.
The doctoral project deals with the development of models and methods for buffer allocation and buffer distribution in series production systems with consolidated buffers. In addition to the production rate and the capital commitment costs, the costs of transporting the workpieces between the production line and the buffer locations must also be taken into account. Since the actual transportation costs depend on the management of the buffers at the operational level, the management strategy must be anticipated in the buffer allocation or distribution at the tactical planning level.
A first modeling approach is based on representing the material flow in the production line as a homogeneous Markov process and analytically calculating the throughput rates of the different buffer configurations. Simple management strategies can be modeled using the structure of the associated transition graph of the Markov chain.
In the further course of the PhD project, heuristic methods for the approximate optimization of buffer allocation or distribution and buffer management will be developed, which are based on a method of admissible directions.